1. Field of the Invention
The systems and methods of this invention generally relate to communication systems. In particular, the systems and methods of this invention relate to equalization using decision feedback.
2. Description of Related Art
In multicarrier modulation, a transmission channel is partitioned into a multitude of sub-channels, each with its own associated carrier. In implementations of multicarrier modulation known as discrete multitone (DMT) transmission, or orthogonal frequency division multiplexing (OFDM), the generation and modulation of the sub-channels is accomplished digitally, using an orthogonal transformation on each of a sequence of blocks, i.e., frames, of the data stream. A receiver performs the inverse transformation on segments of the sampled waveform to demodulate the data. In the implementation of DMT used as the signaling standard for asymmetric digital subscriber lines (ADSL), the transforms used for demodulation and modulation are the Discrete Fourier Transform (DFT) and its inverse, respectively. Further information regarding the asymmetric digital subscriber line standard can be found in the article Asymmetric Digital Subscriber Line (ADSL) Metallic Interface, ANSI T1E1.4/94-007R8, 1994, incorporated herein by reference in its entirety.
In another implementation, referred to as discrete wavelet multitone (DWMT) transmission, a discrete wavelet transform and its inverse are employed as discussed in M. A. Tzannes et al, “The DWMT: A Multicarrier Transceiver for ADSL Using M-Band Wavelets,” ANSI Standard Committee T1E1.4 contribution 93-067, March 1993, M. A. Tzannes, “System Design Issues for the DWMT Transceiver,” ANSI Standard Committee T1E1.4 contribution 93-100, April 1993 and M. A. Tzannes et al, “DMT Systems, DWMT Systems and Digital Filter Banks,” Proc. ICC 1994, all of which are incorporated herein by reference in their entirety.
Thus, in a multicarrier system, a communication path having a fixed bandwidth is divided into a number of sub-bands having different frequencies. The width of the sub-bands is chosen to be small enough to allow the distortion in each sub-band to be modeled by a single attenuation and phase shift for the band. If the noise level in each band is known, the volume of data sent in each band may be optimized by choosing a symbol set having the maximum number of symbols consistent with the available signal to noise ratio of the channel. By using each sub-band at its maximum capacity, the amount of data that can be transmitted in the communication path is maximized.
In practice, such systems are implemented by banks of digital filters which make use of Fast Fourier Transforms (FFT). In the case in which a single data stream is to be transmitted over the communication path is broken into M sub-bands, during each communication cycle, the portion of the data stream to be transmitted is converted to M QAM symbols chosen to match the capacity of the various channels.
The time domain signal to be sent on the communication path is obtained by selecting a QAM point on each sub-carrier and then adding the modulation carriers to form the signal to be placed in the communication path. This operation is normally carried out by transforming the vector of M symbols via the inverse Fourier transform to generate N, where N represents the size of the transform, time domain values that are sent in sequence on the communication path. At the other end of the communication path, the N time domain values are accumulated and transformed via a Fourier transform to recover the original M symbols after equalization of the transformed data to correct for the attenuation and phase shifts that may have occurred in the channels.
One type of problem encountered in transmission systems is intersymbol interference (ISI). When the time domain values are transmitted, the values are spread over time by the impulse response of the system. Often, a guard band is included to prevent previous frames from interfering with subsequent frames, but these guard bands are often too small to be sufficient on their own. Also, values from within the same frame can interfere with each other to cause ISI, sometimes referred to as intersubchannel interference. The time domain equalizer works to shorten the overall length of the impulse response but usually does not remove all of the ISI.
Therefore, the symbol decoded by the subscriber will include interference from other symbols in other sub-bands and/or earlier or later symbols transmitted in the subscriber's sub-band. This type of interference is further aggravated by the high side lobes in the sub-bands provided by the Fourier transform. Further information regarding multicarrier transmission systems can be obtained from U.S. Pat. No. 5,636,246 entitled “Multicarrier Transmission System,” incorporated herein by reference in its entirety.